Modelling the labour
market
Labour supply decisions
The effect of a minimum wage
Modelling the labour market

There is one type of “commodity” that hasn’t
been analysed yet


Labour !!
Although it can be analysed using the same
tools as other markets, the labour market
has some particularities



In terms of the properties of this “commodity”:
welfare aspects are important.
In terms of asymmetric information: it is not a
homogenous good, markets are “segmented”.
Therefore, it is important in terms of policy
Modelling the labour market
The labour supply decision
The classical labour market
Efficiency wages
Monopsony power and the minimum
wage
The labour supply decision

Framework similar to the approach used for
consumer choice and producer decisions


Labour is treated like a regular commodity
Based on an agent deriving utility from
consumption and leisure


Indifference curve based on preference for
consumption (which requires income) and leisure
(free time)
Budget constraint based on working (which uses
up free time but provides and income)
The labour supply decision
The labour supply decision indifference curve
1.
2.
3.
Is strictly convex and decreasing
Corresponds to an utility function U(C,Λ) defined over
consumption (of an aggregate basket) and leisure
Leisure brings utility ⇔ labour brings disutility
Consumption
(C)
Leisure (Λ)
The labour supply decision

The labour supply decision budget
constraint


First of all: Workers can earn an income
independently of supplying labour (unearned
income).
Labour generates a disutility, but this is
compensated by a wage.
Cost of
consumption
C  P  I u  wmax  
Unearned
income
Labour supplied
(defined as leisure
not taken)
The labour supply decision
The labour supply decision budget constraint
Consumption
(C)
I u  w max 
P
B
Maximum consumption strategy
C
I u  w max   
P
Iu
A
Λmax
Maximum leisure strategy
Leisure (Λ)
The labour supply decision
The labour supply decision
Consumption
(C)
The optimal point is
given by the tangency
between the budget
constraint and the
indifference curve
A
Leisure
mU C mU 

P
w
Labour
Λmax
Leisure (Λ)
The labour supply decision
Effect of an increase in unearned income
Consumption
(C)
An increase in unearned
income increases
consumption and leisure
(reduces labour supply)
B
A
Λmax
Leisure (Λ)
The labour supply decision
Effect of an increase in the wage rate
An increase in the wage
rate usually increases
consumption and
reduces leisure
BUT this depends on the
income/substitution
effects !!
An increase can reduce
labour supply
Consumption
(C)
B
A
Λmax
Leisure (Λ)
Modelling the labour market
The labour supply decision
The classical labour market
Efficiency wages
Monopsony power and the minimum
wage
The classical labour market

The supply of labour is given by the
decision process shown above


Aggregated as for other commodities
The demand for labour is known as a
derived demand
It comes from the cost minimisation
decision of the firms, and is derived from
the optimal level of output
  P  Q  TC
 Remember that

The classical labour market

Simplification : Labour is the only input


  P  Q  TC
becomes   P  QL  wL L
Maximisation w.r.t labour gives:

QL 
wL 
 P
 wL  
L 0
L
L
L

On a classical market, the firm is a price
taker on all markets (including labour)
Marginal revenue
product of labour
QL 
P
w
L
wage
The classical labour market
w
Equilibrium on a classical market
Labour
Supply
w*
Labour
Demand
(mRPL)
L*
L
The classical labour market
w
Minimum wage on a classical market
Unemployment
Labour
Supply
wmin
Deadweight
loss
w*
Labour
Demand
(mRPL)
Ld
L*
Ls
L
Modelling the labour market
The labour supply decision
The classical labour market
Efficiency wages
Monopsony power and the minimum
wage
Efficiency wages

Like other markets, the labour market is far from
competitive.

1.
2.
3.
4.
5.

It is in fact one of the most “imperfect” markets
Large number of agents (not for all types of
labour)
Differentiated “product”: variation in skill /ability
Entry / exit is costly/complicated on both sides
Imperfect information on skill/ability
Imperfect mobility of inputs
Has given birth to “labour economics”
Efficiency wages


An example of such developments is the
theory of efficiency wages
The theory of efficiency wages attempts to
explain why:



Some wages can be higher than the market
equilibrium
There is an equilibrium unemployment
I.e. the “minimum wage diagram” seen above
occurs spontaneously on some segments of the
labour market
Efficiency wages

This theory integrates the imperfect information
principal/agent theory seen in week 12 into the
labour market.
 The producer has limited information on the skills



/abilities of the agents.
The producer’s ability to monitor the agent is limited.
The agent clearly has an incentive to “shirk”, i.e.
produce below his ability.
In such a situation, the producer can raise wages
above the market level and increase efficiency of
production at the same time !!
Efficiency wages

Why would wages above market equilibrium
benefit the producer ?





“Worker health” argument (only really valid for low
wages): a higher wage increases the ability to work
Motivation argument: workers feel rewarded, and
more motivated.
Opportunity cost argument (important): workers will
not want to lose the job, and hence shirk less.
Smaller turnover ⇒ lower cost of replacing workers
Signal to market argument: Paying higher wages
allows the producer to attract the more productive
workers
Modelling the labour market
The labour supply decision
The classical labour market
Efficiency wages
Monopsony power and the minimum
wage
Monopsony power and the minimum wage

On a classical market a minimum wage
causes unemployment



This is a typical argument in the media against
minimum wages
This argument depends on the existence of
a competitive market for labour
But is the labour market competitive ?


There are much less demanders (firms) than
suppliers)...
This raises the possibility of Monopsony power
mentioned in week 8.
Monopsony power and the minimum wage

Just like a price ceiling can be used to
reduce monopoly power, a price floor
(minimum wage) can reduce Monopsony
power
mCL  wL  

wL 
 L  wL 
L
The following assumes a single firm
employing all the workforce


This is a simplification
However, it illustrates the potential positive
effect of a minimum wage in this case
Monopsony power and the minimum wage
Monopsony equilibrium
Wages
mCL
Labour Supply
1st : mCL=mRPL
gives L
1st
2nd : given L,
the supply
curve gives w
mPL
w
2nd
Marginal Revenue
Product of Labour
L
Labour
Monopsony power and the minimum wage

Important property of this unemployment




Compared to efficiency wages, here the wage is
below the equilibrium level !
This corresponds to a “worker exploitation” idea
As a result, it is relatively easy to differentiate
the two models.
Also corresponds to different types of
labour: skill-intensive or “homogeneous”

This applies to different labour markets
Monopsony power and the minimum wage
Minimum wage
Wages
mCL
Labour Supply
Wmin >w
gives a
constant mCL
For mCL =
MRPL, L
wmin
w
increases
Marginal Revenue
Product of Labour
L Lmin
Labour
Monopsony power and the minimum wage
Optimal Minimum wage
Wages
mCL
Labour Supply
Workers are paid
at the MPL
No remaining
unemployment
Problem: this
optimal point is
difficult to find
w*min
w
Marginal Revenue
Product of Labour
L
L*min
Labour
Monopsony power and the minimum wage
“Overdoing” the minimum wage
Wages
mCL
Labour Supply
Setting wmin > w*min
creates unemployment
This is because the
market power is overcompensated: classical
unemployment
wmin
w
Marginal Product of Labour
L
Lmin
Labour